We have developed a laser molecular beam epitaxy system for the layer-by-layer growth of oxide thin films. Using this system, we could grow and control oxide thin films of LaAlO$_3$in a molecular layer epitaxy mode on the atomically flat SrTiO$_3$ substrate with a LaAlO$_3$single crystal target. Very clear RHEED oscillations were observed during to growth of a LaAlO$_3$ film for a long period under the optimized conditions of substrate temperature at $650^{circ}C$, oxygen pressure at 1$ imes$10ulcorner torr, and an incident laser fluence of 4.6J/$ extrm{cm}^2$. The height of mono-layer-LaAlO$_3$ film grown during one period of RHEED intensity oscillation was 3.8$AA$.